Exercises: Balancing chemical equations

The industrial synthesis of ammonia is written as $\text{N}_2 + 3\ \text{H}_2 \rightarrow 2\ \text{NH}_3$, as shown in the figure using the particle model:

Interpret it in two ways:

1. a) Using molecules: how many molecules of nitrogen and hydrogen react and how many molecules of ammonia are formed.
2. b) Using moles: how many moles of each gas are consumed when $2\ \text{mol}$ of ammonia are formed.

Count the atoms of each element on both sides of equation $\text{CH}_4 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$, as it is written. The figure shows it using the particle model:

Reason whether it is balanced or not. If it is not, state which elements fail.

Hydrochloric acid is obtained industrially by reacting gaseous hydrogen and chlorine. Balance the equation: $\text{H}_2 + \text{Cl}_2 \rightarrow \text{HCl}$.

Metallic calcium reacts with oxygen in the air to form calcium oxide, quicklime. Balance the equation: $\text{Ca} + \text{O}_2 \rightarrow \text{CaO}$.

A car's catalytic converter finishes burning carbon monoxide, a very toxic gas, transforming it into carbon dioxide. Balance the equation: $\text{CO} + \text{O}_2 \rightarrow \text{CO}_2$.

Sodium is a soft metal that reacts violently with chlorine to form common salt. Balance the equation: $\text{Na} + \text{Cl}_2 \rightarrow \text{NaCl}$.

The thin layer that protects the aluminum parts of an aeroplane from the air is aluminum oxide. The figure shows the particles involved:

Check, by counting the atoms of each element on both sides, whether this equation is balanced: $4\ \text{Al} + 3\ \text{O}_2 \rightarrow 2\ \text{Al}_2\text{O}_3$.

In the electrolysis of water, electric current decomposes it into hydrogen and oxygen gases. Balance the equation: $\text{H}_2\text{O} \rightarrow \text{H}_2 + \text{O}_2$.

Camping gas canisters contain propane, $\text{C}_3\text{H}_8$, which burns with oxygen in the air to form carbon dioxide and water vapour. The figure shows the molecules involved:

Balance the equation by inspection: $\text{C}_3\text{H}_8 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$. Remember to leave oxygen until the end.

The bioethanol mixed with gas, $\text{C}_2\text{H}_6\text{O}$, burns to form carbon dioxide and water. Balance the equation: $\text{C}_2\text{H}_6\text{O} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$. Notice that the fuel itself already contains oxygen in its formula.

Sulphur dioxide coming out of some chimneys is oxidised in the atmosphere to sulphur trioxide, a step prior to the formation of acid rain. Balance the equation: $\text{SO}_2 + \text{O}_2 \rightarrow \text{SO}_3$.

In the laboratory, oxygen can be obtained by heating potassium chlorate, which decomposes into potassium chloride and oxygen. Balance the equation: $\text{KClO}_3 \rightarrow \text{KCl} + \text{O}_2$.

When a piece of aluminum is dropped into a test tube with hydrochloric acid, dissolved aluminum chloride and hydrogen bubbles are formed. Balance the equation: $\text{Al} + \text{HCl} \rightarrow \text{AlCl}_3 + \text{H}_2$.

Car engines produce nitrogen monoxide, $\text{NO}$, which oxidises when released into the air to form the brownish nitrogen dioxide seen in pollution episodes. Balance the equation: $\text{NO} + \text{O}_2 \rightarrow \text{NO}_2$.

When baking a cake, the sodium hydrogen carbonate in the baking powder decomposes with heat into sodium carbonate, water and the carbon dioxide that makes the dough rise. Balance the equation: $\text{NaHCO}_3 \rightarrow \text{Na}_2\text{CO}_3 + \text{H}_2\text{O} + \text{CO}_2$.

The phosphorus on the match head burns with oxygen in the air to form phosphorus(V) oxide. Balance the equation: $\text{P} + \text{O}_2 \rightarrow \text{P}_2\text{O}_5$.

Ethane, $\text{C}_2\text{H}_6$, accompanies methane in natural gas.

1. a) Balance its combustion, $\text{C}_2\text{H}_6 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$, keeping the coefficient of ethane equal to $1$ for now: you will find that the coefficient for oxygen turns out to be a fraction.
2. b) Then multiply all the coefficients by the appropriate number to write the equation with the lowest possible integer coefficients.

Your cells "burn" glucose from the blood in cellular respiration, obtaining energy and releasing carbon dioxide and water. Balance the equation: $\text{C}_6\text{H}_{12}\text{O}_6 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$. Check the result by carefully counting the oxygen atoms on both sides.

Oxy-acetylene torches in workshops burn acetylene, $\text{C}_2\text{H}_2$, with oxygen and reach about $3\,000\ \celsius$.

1. a) Balance the combustion equation: $\text{C}_2\text{H}_2 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}$.
2. b) If a fraction appeared while balancing it, explain how to convert the balanced equation into lowest integer coefficients and write the final equation.

To weld railway tracks, the thermite reaction is used: aluminum powder mixed with iron(III) oxide reacts, giving off so much heat that the iron formed remains molten.

1. a) Balance the equation: $\text{Al} + \text{Fe}_2\text{O}_3 \rightarrow \text{Al}_2\text{O}_3 + \text{Fe}$.
2. b) Explain why it is convenient to balance iron and aluminum first and leave oxygen until the end.

Lavoisier and Priestley studied oxygen by heating mercury oxide, a red powder that decomposes into liquid mercury and oxygen gas. The figure shows how the particles of each substance are formed:

1. a) Balance the equation: $\text{HgO} \rightarrow \text{Hg} + \text{O}_2$.
2. b) Mercury is written as $\text{Hg}$ and not $\text{Hg}_2$, whereas oxygen does have a subscript. Explain, using the particle model, the reason for this difference.

When balancing the combustion of propane, a student wrote: $2\ \text{C}_3\text{H}_8 + 10\ \text{O}_2 \rightarrow 6\ \text{CO}_2 + 8\ \text{H}_2\text{O}$.

1. a) Check, by counting atoms, that their equation respects the conservation of atoms.
2. b) Even so, the teacher marks it as "could be improved". Explain what it means that the coefficients must be the lowest possible integers and rewrite the equation correctly.

In the complete combustion of an unknown hydrocarbon $\text{X}$, the balanced equation is: $2\ \text{X} + 9\ \text{O}_2 \rightarrow 6\ \text{CO}_2 + 6\ \text{H}_2\text{O}$. The figure represents it using the particle model (one molecule of each type):

1. a) Deduce, by counting the carbon and hydrogen atoms that must appear in the products, the molecular formula of $\text{X}$.
2. b) Write the complete equation using the formula found.

The complete combustion of any hydrocarbon $\text{C}_x\text{H}_y$ follows the same pattern.

1. a) Write the balanced general equation in terms of $x$ and $y$: $\text{C}_x\text{H}_y + \left(x + \frac{y}{4}\right)\ \text{O}_2 \rightarrow x\ \text{CO}_2 + \frac{y}{2}\ \text{H}_2\text{O}$, and justify it by counting atoms.
2. b) Apply it to predict how many $\text{O}_2$ molecules are needed to burn one molecule of heptane, $\text{C}_7\text{H}_{16}$, a component of gasoline, and verify the result by balancing its combustion equation.